Problems of existence of the singular spectrum on the continuous spectrum emerges in some mathematical aspects of quantum scattering theory and quantum solid physics. In the latter field, this phenomenon results from physical effects such as the Anderson transitions in dielectrics. In the study of this problem, selfadjoint Friedrichs model operators play an important part and constitute quite a...

We study an initial value problem with fractional Laplacian and a singular integral drift term. This equation quantifies fractal interfaces in statistical mechanics. The singularity of the term is generalization existing results. Making use some important boundedness properties Calder\'on-Zygmund operator \(L_p\) Lipschitz spaces, we obtain local global existence theorems.

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

In this paper, we prove the boundedness of the multilinear commutator related to the singular integral operator in Morrey and Morrey-Herz spaces on homogeneous spaces. 2000 Mathematics Subject Classification: 42B20, 42B25. 1. Preliminaries Sawano and Tanka(see [13]) introduced the Morrey spaces on the non-homogeneous spaces and proved the boundedness of Hardy-Littlewood maximal operators, Calde...

In the present paper, we introduce some singular integral operators, singular quadrature operators and discretization matrices of singular integral equations with Hilbert kernel. These results both improve the classical theory of singular integral equations and develop the theory of singular quadrature with Hilbert kernel. Then by using them a unified framework for various collocation methods o...

We consider the Helmholtz single-layer operator (the trace of the single-layer potential) as an operator on L2(Γ ) where Γ is the boundary of a 3–d obstacle. We prove that if Γ is C2 and has strictly positive curvature then the norm of the single-layer operator tends to zero as the wavenumber k tends to infinity. This result is proved using a combination of (i) techniques for obtaining the asym...